Question

45 points! Please help!

Can the formula S=A1/1-r be used to find the sum of all the terms of each sequence? Explain why or why not.
Sequence One: 5, 1, 1/5, 1/25,...
Sequence Two: 1/32, 1/16, 1/8, 1/4,...
Sequence Three:7, 14, 22, 28,...
Sequence Four:1, -3/2, 9/4, -27/8,...

Answer 1

Sequence One

Explanation:

S = a₁ / (1 − r) is the infinite sum of a geometric series where |r| < 1.

Sequence One: r = 1/5

Sequence Two: r = 2

Sequence Three: not geometric

Sequence Four: r = -3/2

Only Sequence One has |r| < 1.